Accurate and locking-free analysis of beams, plates and shells using solid elements

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-020-01969-0. This paper investigates the capacity of solid finite elements with independent interpolations for displacements and strains to address shear, membrane and volumetric locking in the analysis of beam, plate and shell structures. The performance of the proposed strain/displacement formulation is compared to the standard one through a set of eleven benchmark problems. In addition to the relative performance of both finite element formulations, the paper studies the effect of discretization and material characteristics. The first refers to different solid element typologies (hexahedra, prisms) and shapes (regular, skewed, warped configurations). The second refers to isotropic, orthotropic and layered materials, and nearly incompressible states. For the analysis of nearly incompressible cases, the B-bar method is employed in both standard and strain/displacement formulations. Numerical results show the enhanced accuracy of the proposed strain/displacement formulation in predicting stresses and displacements, as well as producing locking-free discrete solutions, which converge asymptotically to the corresponding continuous problems. The authors gratefully acknowledge the financial support from the Ministry of Science, Innovation and Universities (MCIU) via: the ADaMANT project (Computational Framework for Additive Manufacturing of Titanium Alloy, Proyectos de I+D -Excelencia-, ref. num. DPI2017-85998-P); the SEVERUS project (Multilevel evaluation of seismic vulnerability and risk mitigation of masonry buildings in resilient historical urban centres, ref. num. RTI2018-099589-B-I00); and the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2018-000797-S). Sungchul Kim gratefully acknowledges the support received from the Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) and the European Social Fund (ESF) through the predoctoral FI grants (ref. num. 2019FI_B00727).